3.316 \(\int \frac{e^{\tan ^{-1}(x)}}{1+x^2} \, dx\)

Optimal. Leaf size=4 \[ e^{\tan ^{-1}(x)} \]

[Out]

E^ArcTan[x]

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Rubi [A]  time = 0.031119, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083 \[ e^{\tan ^{-1}(x)} \]

Antiderivative was successfully verified.

[In]  Int[E^ArcTan[x]/(1 + x^2),x]

[Out]

E^ArcTan[x]

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Rubi in Sympy [A]  time = 2.801, size = 3, normalized size = 0.75 \[ e^{\operatorname{atan}{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp(atan(x))/(x**2+1),x)

[Out]

exp(atan(x))

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Mathematica [A]  time = 0.0029576, size = 4, normalized size = 1. \[ e^{\tan ^{-1}(x)} \]

Antiderivative was successfully verified.

[In]  Integrate[E^ArcTan[x]/(1 + x^2),x]

[Out]

E^ArcTan[x]

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Maple [A]  time = 0.003, size = 4, normalized size = 1. \[{{\rm e}^{\arctan \left ( x \right ) }} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp(arctan(x))/(x^2+1),x)

[Out]

exp(arctan(x))

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Maxima [A]  time = 1.34774, size = 4, normalized size = 1. \[ e^{\arctan \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^arctan(x)/(x^2 + 1),x, algorithm="maxima")

[Out]

e^arctan(x)

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Fricas [A]  time = 0.21822, size = 4, normalized size = 1. \[ e^{\arctan \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^arctan(x)/(x^2 + 1),x, algorithm="fricas")

[Out]

e^arctan(x)

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Sympy [A]  time = 1.57426, size = 3, normalized size = 0.75 \[ e^{\operatorname{atan}{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp(atan(x))/(x**2+1),x)

[Out]

exp(atan(x))

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GIAC/XCAS [A]  time = 0.224259, size = 4, normalized size = 1. \[ e^{\arctan \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^arctan(x)/(x^2 + 1),x, algorithm="giac")

[Out]

e^arctan(x)